A15124 | Euclid Guess

Let's consider Euclid's algorithm for finding the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor), where $t$ is a list:

```
<pre class="verbatim"><br></br>function Euclid(a, b):<br></br> if a < b:<br></br> swap(a, b)<br></br><br></br> if b == 0:<br></br> return a<br></br><br></br> r = reminder from dividing a by b<br></br> if r > 0:<br></br> append r to the back of t<br></br><br></br> return Euclid(b, r)<br></br>
```

There is an array $p$ of pairs of positive integers that are not greater than $m$ . Initially, the list $t$ is empty. Then the function is run on each pair in $p$ . After that the list $t$ is shuffled and given to you.

You have to find an array $p$ of any size not greater than $2 \cdot 10^4$ that produces the given list $t$ , or tell that no such array exists.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 10^3$ , $1 \le m \le 10^9$ ) — the length of the array $t$ and the constraint for integers in pairs.

The second line contains $n$ integers $t_1, t_2, \ldots, t_n$ ( $1 \le t_i \le m$ ) — the elements of the array $t$ .

- If the answer does not exist, output $-1$ .
- If the answer exists, in the first line output $k$ ( $1 \le k \le 2 \cdot 10^4$ ) — the size of your array $p$ , i. e. the number of pairs in the answer. The $i$ -th of the next $k$ lines should contain two integers $a_i$ and $b_i$ ( $1 \le a_i, b_i \le m$ ) — the $i$ -th pair in $p$ .

If there are multiple valid answers you can output any of them.